No abstract

We consider a certain class of chance-constrained binary knapsack problem where each item has a normally distributed random weight that is independent of the other items. For this problem we propose an efficient pseudo-polynomial time algorithm based on the robust optimization approach for finding a solution with a theoretical bound on the probability of satisfying the knapsack constraint. Our algorithm is tested on a wide range of random instances, and the results demonstrate that it provides qualified solutions quickly. In contrast, a state-of-the-art MIP solver is only applicable for instances of the problem with a restricted number of items.

The large-scale integration of electric vehicles (EVs) into power systems is expected to lead to challenges in the operation of the charging infrastructure. In this paper, we deal with the problem of an aggregator coordinating charging schedules of EVs with the objective of minimizing the total charging cost. In particular, unlike most previous studies, which assumed constant maximum charging power, we assume that the maximum charging power can vary according to the current state of charge (SOC). Under this assumption, we propose two charging schemes, namely non-preemptive and preemptive charging. The difference between these two is whether interruptions during the charging process are allowed or not. We formulate the EV charging-scheduling problem for each scheme and propose a formulation that can prevent frequent interruptions. Our numerical simulations compare different charging schemes and demonstrate that preemptive charging with limited interruptions is an attractive alternative in terms of both cost and practicality. We also show that the proposed formulations can be applied in practice to solve large-scale charging-scheduling problems.

Abstract--The dynamic tariff (DT) method is designed for the distribution system operator (DSO) to alleviate congestions that might occur in a distribution network with high penetration of distributed energy resources (DERs). Uncertainty management is required for the decentralized DT method because the DT is determined based on optimal day-ahead energy planning with forecasted parameters such as day-ahead energy prices and energy needs which might be different from the parameters used by aggregators. The uncertainty management is to quantify and mitigate the risk of the congestion when employing the DT method, which is achieved by firstly formulating the problem as a chance constrained two-level optimization and then solving the problem through an iterative procedure. Two case studies were conducted to demonstrate the efficacy of the uncertainty management of DT method. Index Terms--Chance constrained program, congestion management, distribution system operator (DSO), distributed energy resources (DERs), uncertainty management.